indeed, I'm glad to see I'm not the only one sick and tired of people calling every minor little issue a "-gate."
just some common sense advice: If you're on your third exchange and still aren't happy, then it's time to come to terms with the notion that perhaps obtaining an iPhone 5s that meets your high expectations just isn't in the cards.
Some might accuse you of having OCD or being too obsessive. Others (and likely yourself) might accuse Apple of having Quality Control that's too poor. But regardless of where the finger is pointed, the outcome stays the same: the phones are still going to rattle.
So, you have a choice to make: be happy with the unit you currently have and accept its flaws, real or perceived. Or, assuming you still can, cut your losses and return the device and get a refund, if you truly feel that this issue is going to prevent you from effectively enjoying and using it.
Once you're on device 4 and still having the same issues, the odds of getting a "perfect" one at number 5, number 10... number 20? Drastically diminish with each successive exchange, and it'll simply be a waste of time and effort to continue.
For what it's worth: there's a small rattle in my iPhone 5s too. My solution? Don't shake the phone. And based on your experienced, they're probably all gonna do that anyway.